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Question

A family has two cars. The first car has a fuel efficiency of
40
miles per gallon of gas and the second has a fuel efficiency of
15
miles per gallon of gas. During one particular week, the two cars went a combined total of
2125
miles, for a total gas consumption of
75
gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

lets assume:

x = number of miles of the 1st car 

y = number of miles of the 2nd car

x/40 = number of gas consumed by 1st car 

y/15 = number of gas consumed by 2nd car

 now we have 

x      + y      = 2125  miles-----> eq1

x/40 + y/15 = 75      gallon of gas----> eq2

we can arrange equations

      x      +      y       = 2125

-15(x/40) - 15(y/15) = -15 * 75   ( after multiply bu -15)

-------------------------------------

(1-3/8)x = 1000----->5/8x =1000----> x = 1600 miles drove by 1st car 

and substitute in eq1 we get y = 525 miles drove by second car

now to calculate how much gas is consumed 

1st car     1600 / 40 = 40 gallon of gas

2nd car    525 / 15 = 35 gallon of gas

 

Best